5x-3-7=9+2x-16
5x-10=2x-7
5x-2x=-7+10
3x=3
X=1
Answer:
As few as just over 345 minutes (23×15) or as many as just under 375 minutes (25×15).
Imagine a simpler problem: the bell has rung just two times since Ms. Johnson went into her office. How long has Ms. Johnson been in her office? It could be almost as short as just 15 minutes (1×15), if Ms. Johnson went into her office just before the bell rang the first time, and the bell has just rung again for the second time.
Or it could be almost as long as 45 minutes (3×15), if Ms. Johnson went into her office just after the bells rang, and then 15 minutes later the bells rang for the first time, and then 15 minutes after that the bells rang for the second time, and now it’s been 15 minutes after that.
So if the bells have run two times since Ms. Johnson went into her office, she could have been there between 15 minutes and 45 minutes. The same logic applies to the case where the bells have rung 24 times—it could have been any duration between 345 and 375 minutes since the moment we started paying attention to the bells!
Step-by-step explanation:
Let's consider that number to be 'x'..
So, twice the number (2x) is 12 greater than than the half of the number.
So the equation will be like,
2x=12+x/2
Solving this further,
2x=(24+x)/2
=> 4x=24+x
=>4x-x=24
=>3x=24
=>x=8..
So the number is "8".
To solve this word problem, we will use the Pythagorean Theorem.
Pythagorean Theorem: a^2 + b^2 = c^2
Our side lengths are 10 and 24ft.
So, we can plug them in for a and b.
10^2 + 24^2 = c^2
100 + 576 = 676
Then, we need to find the square root of 676.
sqrt676) = 26
So, the missing length or the hypotenuse is 26 feet.
Therefore, we require 26 feet of string to measure the length of the hypotenuse in which the room is split in half.
Answer: AB is 15
Step-by-step explanation: First, you need to draw a picture and label the parts of the line: AB=5x-15; BC= 3x-5; AC =28. Because of the segment addition postulate, you set the equation to be 5x-15+3x-5=28. Then you solve:
5x-15+3x-5=28
Add like terms:
8x-20=28
Add 20 to both sides
8x=48
Divide by 8
x=6
Now, you need to find the measure of AB, so you plug the 6 into the x variable for 5x-15
5(6)-15
30-15
AB=15